Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 49   b = 43   c = 6.4

Area: T = 51.09993385476
Perimeter: p = 98.4
Semiperimeter: s = 49.2

Angle ∠ A = α = 158.2200392687° = 158°12'1″ = 2.76111177303 rad
Angle ∠ B = β = 19.01994215818° = 19°1'10″ = 0.33219515284 rad
Angle ∠ C = γ = 2.78801857317° = 2°46'49″ = 0.04985233948 rad

Height: ha = 2.08656872877
Height: hb = 2.37767134208
Height: hc = 15.96985432961

Median: ma = 18.56769060427
Median: mb = 27.54550540025
Median: mc = 45.98765197639

Inradius: r = 1.0398604442
Circumradius: R = 65.97334567183

Vertex coordinates: A[6.4; 0] B[0; 0] C[46.325; 15.96985432961]
Centroid: CG[17.575; 5.32328477654]
Coordinates of the circumscribed circle: U[3.2; 65.89658040497]
Coordinates of the inscribed circle: I[6.2; 1.0398604442]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 21.87996073134° = 21°47'59″ = 2.76111177303 rad
∠ B' = β' = 160.9810578418° = 160°58'50″ = 0.33219515284 rad
∠ C' = γ' = 177.2219814268° = 177°13'11″ = 0.04985233948 rad

Calculate another triangle




How did we calculate this triangle?

a = 49 ; ; b = 43 ; ; c = 6.4 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 49+43+6.4 = 98.4 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 98.4 }{ 2 } = 49.2 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 49.2 * (49.2-49)(49.2-43)(49.2-6.4) } ; ; T = sqrt{ 2611.14 } = 51.1 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 51.1 }{ 49 } = 2.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 51.1 }{ 43 } = 2.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 51.1 }{ 6.4 } = 15.97 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 43**2+6.4**2-49**2 }{ 2 * 43 * 6.4 } ) = 158° 12'1" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 49**2+6.4**2-43**2 }{ 2 * 49 * 6.4 } ) = 19° 1'10" ; ; gamma = 180° - alpha - beta = 180° - 158° 12'1" - 19° 1'10" = 2° 46'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 51.1 }{ 49.2 } = 1.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 49 }{ 2 * sin 158° 12'1" } = 65.97 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 43**2+2 * 6.4**2 - 49**2 } }{ 2 } = 18.567 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.4**2+2 * 49**2 - 43**2 } }{ 2 } = 27.545 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 43**2+2 * 49**2 - 6.4**2 } }{ 2 } = 45.987 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.